According to reports citing the China Manned Space Engineering Office, parts of the rocket re-entered the atmosphere at 10:24 a.m. local time at longitude 72.47 degrees east and latitude 2.65 degrees north.
The Long March 5B - comprising one core stage and four boosters - lifted off from China's Hainan island on April 29 with the unmanned Tianhe module, which contains what will become living quarters on a permanent Chinese space station.
Its 18-tonne main segment is now in freefall and experts have said it is hard to say precisely where and when it will re-enter the atmosphere.
By early Sunday morning the latest prediction for when re-entry would happen was 190 minutes either side of 2.11pm (New Zealand time) today (0211 GMT), the EU Space Surveillance and Tracking (EUSST) said.
The Pentagon said the descent of the Chinese rocket was being tracked by U.S. Space Command.
It added that most of the segment disintegrated and was destroyed during re-entry.
That's because the 23-ton rocket core, which is about 100 feet long and 15 feet wide, was whizzing around the planet at about 18,000 miles per hour, inching its way toward the surface before building friction upon reentry to the atmosphere.
Howard said the United States was tracking the rocket segment but "its exact entry point into the Earth's atmosphere can not be pinpointed until within hours of its re-entry".
"It makes the Chinese rocket designers look lazy that they didn't address this", said McDowell, a member of the Harvard-Smithsonian Center for Astrophysics.
"We call it the Chinese rocket because it comes from CHINA", comedians the Hodge Twins joked late Saturday.
"Given the size of the object, there will necessarily be big pieces left over", said Florent Delefie, an astronomer at the Paris-PSL Observatory.
The core stage of the first Long March 5B that returned to Earth a year ago weighed almost 20 tonnes, surpassed only by debris from the Columbia space shuttle in 2003, the Soviet Union's Salyut 7 space station in 1991, and NASA's Skylab in 1979.
McDowell said that although there was no need to worry "too much", the rocket's design needed a re-think to stop such a scenario happening again.
Chinese Foreign Ministry spokesman Wang Wenbin said Friday that the rocket was unlikely to cause damage.